"Princess Leia, the yodel of life" is neither the title of a fan fiction1 nor a sound Luke Skywalker has ever made. What it is, is a bizarre, non-sequitur phrase somewhat similar to "All your base are belong to us" used to confuse those who don't know what it's from. To be fair, it's actually impossible to use this phrase in context, since it was non-sequitur to begin with.
"Princess Leia, the yodel of life" is a line from an infamous series of animations called "animutations", done by Neil "Trapezoid" Cicierega. It first appeared in Hyakugojyuuichi2 as an intentional mondegreen: think "Excuse me while I kiss this guy", except done on purpose. Hyakugojyuuichi, as one might be able to tell from the title, is a Japanese song that contains no English lyrics. So far as I know, Neil Cicierega doesn't speak Japanese, but apparently thought it would be funny to try and match some English lyrics as closely as possible to the sounds of the Japanese words. The results were brilliant in their surrealism, the animutations became widely popular, and the phrase entered the lexicon of those seeking to confuse the uninitiated.
This isn't the only running joke from Hyakugojyuuichi that has made appearances in other animutations. Pee Wee Herman, Colin Mochrie, Harry Potter, Mr. Bean, some guy with a stretched-out neck, and intentionally poorly photoshopped images of people twisted and drawn over to look monstrously deformed have become a staple of the art form. They also contain animated GIFs of people dancing, images flipped back and forth as a cheap and easy substitute for motion, and rapid-fire pop culture references and fake subliminal messages that are often too fast to even take in on the first viewing. But the overriding theme remains intentionally cheap, shoddy animation put together mostly with images downloaded from around the Internet, set to songs in a foreign language with absolutely no attempt to make any sort of logical connection between the original meaning of the song and the animations which assault3 the viewer.
Since Hyakugojyuuichi, "Princess Leia, the yodel of life" has made several other appearances, both in Neil Cicierega's animutations and the "fanimutations" made by other animators in his style, usually as a sign in the background paying homage to the animutation that started the craze. Below, I have transcribed the original Japanese lyrics, Neil Cicierega's mondegreens, and the real English translation. The Japanese and English lyrics were taken from Codepie's Hyakugojyuuichi writeup, while Neil Cicierega's lyrics were taken from the animutation's subtitles.
Kimi-tachi to no deai wa zenbu
TV says donuts are high in fat, kazoo
I remember all of them well
Chanto oboete 'ru
Found a hobo in my room
My first encounters with you guys
Kizutsukeatta koto mo atta kedo
It's Princess Leia, the yodel of life
There were also painful moments but
Sore wa (e~to) wasureta
Give me my sweater back, or I'll play the guitar
Speaking of which (uhhh) I forgot
Come to think of it, the real lyrics don't make much sense either.
1. At least it wasn't a fan fiction at the time this was written. Who knows what Jurph might have accidentally inspired.
2. Hyakugojyuuichi means "a hundred and fifty-one", and I understand that it was used as the theme song for the Pokémon cartoon. A hundred and fifty-one refers to the number of different Pokémon in the series when it first started (there are many more now).
3. Assault is the best word I can think of to describe the way these images, sometimes disturbing and always senseless, are thrown up on the screen one after another without giving the viewer a chance to breathe. It's the animation equivalent of a cluster bomb.